How to rig a chest lid
One possibility:


Add a bone that begins in the rotation axis. Any other object will do as well because I don't use a rig but simply a parent/child.

Parent the bone to the top of the chest and the bottom of the chest to the bone.

Lock the location of the bone and two of the rotation axes (depends on how your bone is rotated).


 

Now you can select the bone and press R to open and close the chest independent of the chests position or rotation.



Note that you don't even need a third object for that (bone). If the top's origin is on the rotation axis then you can parent directly and lock position as well as two rotation axes.